Two balls of same radius and weight are suspended on threads so that their surfaces are in contact. A total charges of Q=4 x 10^-7 C is given to the balls, makes them repel each other to an angle of 60º. The angle of divergence becomes 54º, when balls are immersed in kerosene. Find the density (s) of the material of the balls if the distance from the point of suspension to the centre of the ball is 0.2m. [Density of kerosene is 800 kg/m^3, dielectric constant k=2, tan27º=0.5]
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Thus the density is l1 = 2559 kg / m^3
Explanation:
Given data:
- Q = 4 x 10^-7 C
- Angle = 60º
- angle of divergence = 54º
- Point of suspension = 0.2 m
Solution:
- W = T cos α
- F = T sin α
Dividing equation (ii) by (i)
F1 / W = tan α
F1 = w tan α = [ 1 / 4 πεo ] (qo^2 / 4 ) / 4 l^2 sin^2 α ]
W = [ 1 / 4 πεo ] ( qo^2 / 4 ) / 4 l^2 sin^2 α . tan α ]
W = 0.0156 N
W = mg
m = w / g = 0.0156 / 9.8 = 1.592 Kg
Now
W = W (B) / W = sin^2 α tan α / K sin^2 α tan α = l1 - ;2 / l1
W = 1 - l2 / l1
l1 = l2 k sin^2α tanα / k sin^2 α2 + tan α2 - sin^2 α . tanα = 2559 kg / m^3
Thus the density is l1 = 2559 kg / m^3
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